Re: TECH: lambda and "ka" revisited

[Chris Bogart <cbogart@QUETZAL.COM>]

>Quine's notation is "x[x is a dog]" and "xy[x is a dog of breed y]".  Here
>x and y are regular logical variables, and this construct binds them.

[...]
>
>3)      le ka da de xe'u da gerku de

How would we use this in a sentence?  The property refers to two entities;
would it be something like {lei re nanmu cu ckaji leka da de xe'u da pendo
de}?  I think {lei} must be wrong here because there's only one entity
(consisting of 2 men); but {le} would be wrong too, because it would be
decomposable into {le pa nanmu cu ckaji leka da de xe'u da pendo de} and {le
drata nanmu ...}.

I don't know about lambda in logical theory but I know how it's used in
Lisp.  The whole lambda expression, which tells you what it's arguments are
then what their relationship should be, can be substituted wherever you
would normally use a named function (i.e. brivla).  The analogy with Lisp
would indicate that we could use it this way (brackets [] surround
lambda-expressions for emphasis and clarification):

   pa nanmu cu [ka da de xe'u da pendo de kei] le drata nanmu

which would be equivalent to {pa nanmu cu pendo le drata nanmu} -- but it
requires that {ka}'s places be defined by the {xe'u} clause.  This is a long
way of saying the same thing, but it makes a nice formal way to define new
lujvo:

   ca'e sezpendo cei [ka da xe'u da pendo da]

...or pro-bridi

   mi do broda cei [ka da de xe'u da de zmadu leka gleki kei] .i do la alis.
broda .i la alis. la djak. broda .i ...

Looking at things this way, then, {le [ka da de xe'u da pendo de]} would be
identical in meaning to {le pendo}, and {le SE [ka da de xe'u da pendo de]}
would mean {le SE pendo}, which strongly conflicts with my current
understanding of how {leka} is used.

So I guess the upshot of all my rambling here is I'm confused about how
Lisp's notion of lambda functions can exactly apply to {ka}.  Of course, if
Lisp's lambda functions don't work similarly to Quine's, then I'm barking up
the wrong tree entirely, and maybe I need to read Quine...

>We can't just have a new variable "xe'u" as a sumti by itself, because
>the bound variable may need recycling:
>
>12)     do ckaji le ka ga xe'u da xirma gi lo xirma cu citka da
>        You have-as-property the attribute-of
>                either (you are-a-horse) or (some horse(s) eat you)
>        You are either a horse or horse-fodder.

Don't we have the same problem with {ke'a}:

  la djan. poi ga ke'a xirma gi lo xirma cu citka ke'a
[or would it be something like:]
  la djan. poi ga ke'a goi da xirma gi lo xirma cu citka da


PS how do {nu} and other abstractors fit into this picture?

                     ____
 Chris Bogart        \  /  ftp://ftp.csn.net/cbogart/html/homepage.html
 Boulder, CO          \/   cbogart@quetzal.com